Consider proportional-only control of the stirred-tank heater control system in fig. e11.13. the temperature transmitter has a span of 50 ∘f and a zero of 55 ∘f. the nominal design conditions are t = 80 ∘f and ti = 65 ∘f. the controller has a gain of 5, while the gains for the control valve and current-to-pressure transducer are kv = 1.2 (dimensionless) and kip = 0.75 psi/ma, respectively. the time constant for the tank is τ = 5 min. the control valve and transmitter dynamics are negligible. after the set point is changed from 80 to 85 ∘f, the tank temperature eventually reaches a new steady-state value of 84.14 ∘f, which was measured with a highly accurate thermometer. (a) what is the offset? (b) what is the process gain k2? (c) what is the pressure signal pt to the control valve at the final steady state